Structural instability of 𝑒𝑥𝑝(𝑧)

Devaney, Robert L.

doi:10.1090/S0002-9939-1985-0787910-2

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ISSN 1088-6826(online) ISSN 0002-9939(print)

Structural instability of ${\rm exp}(z)$

Author: Robert L. Devaney
Journal: Proc. Amer. Math. Soc. 94 (1985), 545-548
MSC: Primary 58F12; Secondary 30D05, 58F10
MathSciNet review: 787910
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Abstract: The entire function $\operatorname{exp}\left( z \right)$ has a Julia set equal to the whole plane. We show that there are complex $\lambda$ 's near 1 such that $\lambda {e^z}$ has an attracting periodic orbit. Hence ${e^z}$ is not structurally stable.

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